Question
Consider the partially ordered set $(X, \subseteq)$ of subsets of the set $X=\{a, b, c\}$ of three elements. How many linear extensions are there?
Step 1
The set \( X = \{a, b, c\} \) has \( 2^3 = 8 \) subsets, which are: \[ \emptyset, \{a\}, \{b\}, \{c\}, \{a, b\}, \{a, c\}, \{b, c\}, \{a, b, c\}. \] Show more…
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